S. C. Ward *, and M.B. Hursthouse a. a School of Chemistry, University of Southampton, SO17 1BJ, UK. Introduction There is currently consideratble interest in the use of salts in the pharmaceutical industry because properties of the solid forms can be modified without altering the desired effect of the drug [1]. Salt formation is essentially a three component system involving an acid (A), a base (B) and one or more solvents. A salt is formed by the transfer of a proton (H+) from an acid (A) to a base (B): A-H + B → (A-)(B+-H). In order to assist choice of components in salt selection a number of empirical rules have been devised, such as the ‘rule of three’. This states that salt formation generally requires a difference of at least three pK a units between the conjugate base and the conjugate acid, pK a (Base) - pK a (Acid) ≥ 3, where pKa is the ability of an ionisable group to donate a proton (H+) in an aqueous medium. Although such rules are valuable guidelines, as far as we are aware no detailed study has been made of the reliability and/or basis of these empirical procedures. A carefully planned set of experiments may lead to a more scientific method for assessing the viability of salt formation, rather than relying on trial and error. A set of descriptors that describe molecular properties relevant to salt formation have been identified. Initially a collection of salt forming acids were assembled from the Cambridge Structural Database [2], and other sources, and their descriptor values calculated. These acids define a chemical space from which the compounds for the experiments can be chosen. The experiments aim to explore this chemical space whilst building statistical models that will allow an understanding of how the descriptors affect salt formation. Descriptors We are investigating an approach in which a statistical model, called a response surface model [3], is fitted to the data from a designed experiment. The fitted model may then be used to predict combinations of acids and bases that are likely to produce a salt. Due to the fact that there is a wide variety of choices for the acid or the base, a set of chemical descriptors was sought that could be used to characterise the chemical space of interest and to form the statistical model. The chosen descriptors should represent key aspects of the molecular structure, which relate to its salt forming ability. A shortlist of such descriptors was eventually chosen that were tabulated in the literature or easily calculated. As a starting point, an initial set of 67 acids was obtained using the CSD. Values for the selected descriptors were either found in the literature or calculated using software such as HyperChem [4]. Values for a total of ten descriptors were investigated. Figure 1 shows a matrix of plots of all the two-dimensional projections (scatter plots) of the values of the ten descriptors (labelled X1 to X10 for simplicity) for the acids. These scatter plots show the relationship between pairs of descriptors for the available acids. A high proportion of points along the diagonal indicates a strong correlation between two descriptors. Descriptors were then removed from the model to eliminate highly correlated pairs. This resulted in descriptors X1, X2, X3, X5, together with either X8 or X9. The next step in the process was to extend the set of acids to obtain better coverage of salt formation space. This was achieved by first identifying regions in the descriptor space where acids were sparse and then finding additional acids in these regions. Systematic Study into the Salt Formation of Functionalised Organic Substrates For our initial set of 67 compounds, and using the descriptors X1, X2, X3, X5 and X8, Figure 2 shows the two-dimensional projections of a 24 point coverage design. The points in the coverage design are chosen to ensure that each unselected compound is as close to a selected compound as possible, giving similar, but less dense, projections compared with Figure 1. Experimental Design Experimental Results A set of carboxylic acids and a set of bases were selected to allow a good coverage of the descriptor values. As an example we will consider 1-phenylcyclopentanecarboxylic acid. 1-Phenylcyclopentanecarboxylic acid has a pK a value of 4.39 and there is only one reported form [5] in the CSD. No organic salts or co-crystals of this acid were found on the CSD. Tables 1 and 2 below show the results when this acid was combined with a selection of nine of the bases in identical conditions BasepK a Product 2-amino-4-methylpyridine7.38Salt 2-amino-5-nitropyridine2.82Parent 2-aminopyridine6.67Salt 2,2-bipyridine4.40Parent 2,4-diamino-6- hydroxypyrimidine 3.96Parent 3,5-dichloropyridine0.66Parent 2-aminopyrimidine3.86Co-crystal 4-aminopyridine9.25Salt hydrate 4-dimethylaminopyridine9.52Salt hydrate A salt is taken to be an A-B composite in which proton transfer has occurred: A-H + B → (A-H) + (B) - A co-crystal is taken to be an A-B composite in which no proton transfer has occurred: A-H + B → (A-H)(B) 2-Aminopyridine 4-Dimethylaminopyridine Table 1. Results from nine bases with 1-phenylcyclopropanecarboxylic acid BaseCrystal Data 2-amino-4- methylpyridine Monoclinic, P2 1 /ca = (9) Å  = 90° Z = 4b = 6.386(16) Å  = (9)° V = 1583(4) Å 3 c = 25.16(2) Å  = 90° 2-amino- pyridine Triclinic, P-1a = (13) Å  = (15)° Z = 2b = (3) Å  = 84.14(2)° V = 729.5(3) Å 3 c = (2) Å  = (17)° 2-amino- pyrimidine Monoclinic, P2 1 /na = 9.138(3) Å  = 90° Z = 4b = (8) Å  = 98.05(3)° V = (12) Å 3 c = (5) Å  = 90° 4-amino- pyridine Triclinic, P-1a = 6.260(8) Å  = 67.32(3)° Z = 4b = (8) Å  = 88.56(8)° V = 1705(2) Å 3 c = (6) Å  = 83.77(14)° 4- dimethylamino- pyridine Monoclinic, P2 1 /na = (7) Å  = 90° Z = 4b = (4) Å  = (12)° (6) Å 3 c = (4) Å  = 90° Table 2. Crystallographic data for the five salts/co-crystals from nine bases Discussion 2-Amino-4-methylpyridine 2-Amino-4-methylpyridine crystallised out with 1- phenylcyclopentanecarboxylic acid as a salt in a 1:1 ratio. The pK a difference in this instance is 2.99 so it is potentially on the borderline of salt/co-crystal formation The molecules from two infinite one- dimensional chains with a base vector of [ 0 1 0], with each acid forming three hydrogen bonds. Acid centroid Base centroid Acid in chain 1 Base in chain 1 Acid in chain 2 Base in chain 2 Packing down a-axis H-bonding of centroids down a-axis H-bonding of centroids down c-axis H-bonding of centroids down b-axis 2-Aminopyrimidine Acid centroid Base centroid H-bonding of centroids down c-axis H-bonding of centroids down b-axis H-bonding motif down a-axis The compounds crystallised out as a 1:1 salt and the molecules are linked via hydrogen bonding to form a 4-membered ring with alternating acid base molecules with the acid molecules forming three hydrogen bonds. The difference in pK a between the acid and base is 2.28 so the rule of three suggests that a co-crystal should form although as shown here a rule of two may be more appropriate Acid centroid Base centroid H-bonding motif down a-axis H-bonding of centroids down a-axis H-bonding of centroids down b-axis H-bonding of centroids down c-axis The compounds crystallised out together as a co-crystal in a 1:1 ratio. Two 4-membered hydrogen bonded chains are formed which pack together as illustrated in the diagrams above. This hydrogen bond motif is similar to that found in the acid but the dimer is extended to incorporate two base molecules in-between. The compounds crystallised out together as a salt hydrate in a 1:1:1 ratio. The molecules hydrogen bond to form four infinite chains with a base vector of [1 0 0]. Each chain is made up of alternating molecules of water and acid with an extra branch to the base molecule from the acid.The acid molecule forms two hydrogen bonds. Packing down a-axis H-bonding of centroids down a-axis Acid centroid Base centroid Water centroid Molecules in chain 1 Molecules in chain 2 Molecules in chain 3 Molecules in chain 4 H-bonding of centroids down b-axis 4-Aminopyridine and 1-phenylcyclopentanecarboxylic acid crystallised out as a salt with water in a 1:1:2, acid:base:water ratio with a Z’=8 giving eight different centroids. The eight molecules hydrogen bond to form an infinite two-dimensional network in the plane ( 0 1 0). Each sheet consists of water molecules in the middle sandwiched between the bulky acid molecules on the top and bottom of the sheet with base molecules linking the rings of acid and water. The acid molecule is unique in this structure in that it forms five hydrogen bonds, one trifurcated and one bifurcated hydrogen bond. H-bonding of centroids down a-axis H-bonding of centroids down c-axis H-bonding sheet down a-axis 4-Aminopyridine Acid centroid 1 Acid centroid 2 Base centroid 1 Base centroid 2 Water centroid 1 Water centroid 2 Water centroid 3 Water centroid 4 Hydrogen bonded chain A set of descriptors for investigating salt formation has been identified and these descriptors have now be used in experiments to investigate the properties needed for salt formation to occur. In the case outlined, two of the bases formed salts, two of the bases formed salt hydrates, one base formed a co-crystal and four of the bases failed to crystallise out with the acid. Where a new product was identified a co-crystal was observed when the difference in pK a was below 2 and a salt was observed when the difference in pK a was above 2. This indicates that the rule of three (or two in this case) is appropriate for predicting whether a salt or co- crystal form but other factors need to be taken into consideration to determine whether a new product will form in the first place. It is hoped that the employment of descriptors for salt formation space will allow us to identify what these factors are. Figure 1. Two-dimensional projections for X1 – X10. Figure 2. Two-dimensional projections for a coverage design for five descriptors. Acknowledgements We gratefully acknowledge the support of the EPSRC e-Science programme (GR/R67729, Combechem) along with AstraZeneca in Mölndal, Sweden. References 1. S. M. Berge, L. D. Bighley, and D. C. Monkhouse, J. Pharm. Sci., 1977, 66, 1. 2.F. H. Allen, Acta Crystallogr. Sect. B, 2002, 58, R. H. Myers and D. C. Montgomery, Response Surface Methodology (2nd ed.), 2002, New York:Wiley. 4.HyperChem, Inc. 115 NW 4th Street, Gainsville, Florida,32601, USA. 5.T. N. Margulis, Acta Crystallogr. Sect. B, 1975, 31, 1049.